The present disclosure relates to the novel utilization of the well-established photoelasticity principles to the design, analysis, fabrication, and testing of mechanical elements, such as elements used to construct trusses. More particularly, the present disclosure relates to a method and apparatus for enhancing visualization of mechanical stress in structural elements.
The science of photoelasticity has a long history, dating back to Brewster's investigations in 1816. Neumann further developed the science to include formulas for strain in terms relevant to photoelasticity. Maxwell extended Neumann's formulas in terms of stress.
A number of tools are available for evaluating strength of materials, as well as mechanical stress and strain occurring in objects under load before a mechanical element is fabricated. Such tools include mold analysis software, finite element analysis (FEA) software, and traditional analytical techniques taught in most Strength of Materials courses. Mold analysis software models the temperature variations or pressure drop variations, due to viscosity of polymer flow front, that is likely to occur in parts during a molding process. FEA software uses a mathematical model of a structure and the computational power of the computer to determine theoretical stress and strain values that occur through the structure under applied loads. Various input parameters, such as the magnitude and direction of the applied load and the material from which the structure is made, are selected to perform FEA. Traditional analysis utilizes appropriate mechanical element material properties, geometry, loading, and constraints to produce estimates on stress and strain levels.
Polariscopes typically have one or more light sources that shine light through a pair of spaced, polarized filters between which is placed the photoelastic object to be evaluated. The polarizing filter closest to the light source is typically called the polarizer and produces emergent light that is plane polarized. The polarizing filter farthest from the light source is typically called the analyzer. As light passes through the polarizer and a loaded specimen, the light wave is split into two orthogonal components. One of the light wave components coincides with the maximum stress plane, while the other component coincides with the minimum stress plane. Since the two light wave components travel at different speeds, they experience a relative retardation. The analyzer allows these two light wave components to pass through parallel to the analyzer's polarizing axis, thereby giving an optical method to deduce the difference between the two principal stresses. When a white light source is utilized in the polarizer, colored bands of light, called isochromatics, appear in fringe patterns. Applying a load to the photoelastic object situated between the filters produces visible isochromatic fringe patterns from which the stress and strain within the object can be deduced. Each isochromatic band is associated with a particular stress level.
There exist two major types of polariscopes in general usage, including a transmission Polariscope and a reflection Polariscope. Transmission polariscopes are used to visually evaluate stresses in thin three-dimensional objects made of photoelastic or birefringment materials, which are transparent or semi-transparent materials such as polycarbonate or acrylic (PMMA). Non-transparent objects can also be evaluated using photoelastic principles through the addition of coatings consisting of a reflective base coat and a top coating of photoelastic material allowing reflection photoelasticity. Maxwell's stress-optic law enables the stress components at a particular location to be analyzed.
Conventional polariscopes and photoelastic materials are sometimes used in academic settings and in industry to gain an understanding of stress and strain formation in individual structural elements or assemblies of structural elements. Trusses and other multi-link structural assemblies typically include elements having continuous or solid cross-sections. However, when using a polariscope to evaluate these elements, it is extremely difficult to discern visually the stress states occurring in the photoelastic elements having such cross-sections because, when loads are applied to these elements, the color changes between adjacent isochromatic bands are fairly subtle.
Characteristics inherent in molding processes have an effect on stress formation in parts made by the molding process. Such characteristics include, for example, temperature variations in a mold cavity during the molding process, pressure drops due to viscosity variations of polymer flow front in the mold cavity, and knit lines formed when slightly cooled plastic flows together from multiple directions in a mold cavity. The location of the gates through which material is injected into a mold cavity affects these various molding characteristics as well. After a molded part cools, there are residual stresses in the molded part due to these various molding characteristics.